Intro to Step Functions

Front

What is a step function?

Back

A step function is a piecewise constant function that jumps from one value to another without taking on any values in between.

Front

How does a step function differ from a continuous function?

Back

A step function has distinct jumps between values, while a continuous function has no breaks or jumps and can take on any value within a range.

Front

What is the value of y when x = -2 in the step function defined as y = 4 for x < 0?

Back

4

Front

What is the value of y when x = 0 in the step function defined as y = 2 for x = 0?

Back

2

Front

How do you determine the value of a step function at a given point?

Back

Evaluate the function based on the defined intervals for the input value.

Front

What is the postage cost for a letter that weighs 6 ounces if the cost is 48 cents for weights between 5 and 7 ounces?

Back

48 cents

Front

What is the postage cost for a letter that weighs 2.1 ounces if the cost is 43 cents for weights between 2 and 3 ounces?

Back

43 cents

Front

How can you represent a step function graphically?

Back

A step function is represented by a series of horizontal line segments that jump vertically at specified points.

Front

What is the cost to rent a Karaoke machine for 3 days if the cost is $100 for 3 days?

Back

$100

Front

What is the general formula for a step function?

Back

A step function can be expressed as f(x) = c_i for x in [a_i, b_i) where c_i is the constant value in the interval [a_i, b_i).